Subgroups — C₃×C₅×#1819 #14274853

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#379	C₂	1	2	yes	maximal
3	C₃×C₅×#342	C₂	1	4	yes	maximal, complemented
4	C₅×#1819	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₂³×C₃×C₄×C₅	C₄	1	2	yes	complemented
7	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
8	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
9	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	complemented
10	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
11	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
12	C₃×#1819	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
14	C₅×#379	C₂×C₃	1	2	yes	—
15	C₅×#342	C₂×C₃	1	4	yes	complemented
16	C₂⁴×C₃×C₅	—	2	4	no	—
17	C₂⁴×C₃×C₅	—	4	4	no	—
18	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
19	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
20	C₂⁴×C₃×C₅	D₄	1	4	yes	—
21	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
22	C₂²×C₃×C₄×C₅	—	2	2	no	—
23	C₂²×C₃×C₄×C₅	—	2	2	no	—
24	C₂²×C₃×C₄×C₅	—	2	4	no	—
25	C₂²×C₃×C₄×C₅	—	4	4	no	—
26	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
27	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
28	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
29	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
30	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
31	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
32	C₃×#379	C₂×C₅	1	2	yes	—
33	C₃×#342	C₂×C₅	1	4	yes	complemented
34	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₃×C₄	1	2	yes	complemented
36	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
37	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
38	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	2	yes	complemented
39	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
40	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
41	#1819	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³×C₃×C₅	—	2	4	no	—
43	C₂³×C₃×C₅	—	2	2	no	—
44	C₂³×C₃×C₅	—	2	8	no	—
45	C₂³×C₃×C₅	—	2	2	no	—
46	C₂³×C₃×C₅	—	2	8	no	—
47	C₂³×C₃×C₅	—	4	2	no	—
48	C₂³×C₃×C₅	—	4	4	no	—
49	C₂³×C₃×C₅	—	4	2	no	—
50	C₂³×C₃×C₅	—	4	16	no	—
51	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
52	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
53	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
54	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
55	C₂³×C₃×C₅	#41	1	4	yes	—
56	C₂×C₃×C₄×C₅	—	2	4	no	—
57	C₂×C₃×C₄×C₅	—	4	4	no	—
58	C₂×C₃×C₄×C₅	—	4	4	no	—
59	C₂×C₃×C₄×C₅	—	4	4	no	—
60	C₂×C₃×C₄×C₅	—	4	8	no	—
61	C₂×C₃×C₄×C₅	—	4	4	no	—
62	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
63	C₂³×C₃×C₄	C₄×C₅	1	2	yes	complemented
64	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
65	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
66	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	2	yes	complemented
67	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
68	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
69	C₂⁴×C₅	—	2	4	no	—
70	C₂⁴×C₅	—	4	4	no	—
71	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
72	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
73	C₂⁴×C₅	C₃×D₄	1	4	yes	—
74	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
75	C₂²×C₄×C₅	—	2	2	no	—
76	C₂²×C₄×C₅	—	2	2	no	—
77	C₂²×C₄×C₅	—	2	4	no	—
78	C₂²×C₄×C₅	—	4	4	no	—
79	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
80	C₅×C₂²⋊C₄	—	2	4	no	—
81	C₅×C₂²⋊C₄	—	2	4	no	—
82	C₅×C₂²⋊C₄	—	2	8	no	—
83	C₅×C₂²⋊C₄	—	4	8	no	—
84	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
85	#379	C₂×C₃×C₅	1	2	yes	—
86	#342	C₂×C₃×C₅	1	4	yes	complemented
87	C₂²×C₃×C₅	—	2	8	no	—
88	C₂²×C₃×C₅	—	2	2	no	—
89	C₂²×C₃×C₅	—	2	2	no	—
90	C₂²×C₃×C₅	—	2	2	no	—
91	C₂²×C₃×C₅	—	2	4	no	—
92	C₂²×C₃×C₅	—	2	2	no	—
93	C₂²×C₃×C₅	—	2	4	no	—
94	C₂²×C₃×C₅	—	4	4	no	—
95	C₂²×C₃×C₅	—	4	16	no	—
96	C₂²×C₃×C₅	—	4	4	no	—
97	C₂²×C₃×C₅	#99	1	4	yes	—
98	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₃×C₅	#117	1	2	yes	—
100	C₂²×C₃×C₅	#123	1	4	yes	—
101	C₃×C₄×C₅	—	4	4	no	—
102	C₃×C₄×C₅	—	8	4	no	—
103	C₂⁴×C₃	—	2	4	no	—
104	C₂⁴×C₃	—	4	4	no	—
105	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
106	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
107	C₂⁴×C₃	C₅×D₄	1	4	yes	—
108	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
109	C₂²×C₃×C₄	—	2	2	no	—
110	C₂²×C₃×C₄	—	2	2	no	—
111	C₂²×C₃×C₄	—	2	4	no	—
112	C₂²×C₃×C₄	—	4	4	no	—
113	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
114	C₃×C₂²⋊C₄	—	2	4	no	—
115	C₃×C₂²⋊C₄	—	2	4	no	—
116	C₃×C₂²⋊C₄	—	2	8	no	—
117	C₃×C₂²⋊C₄	—	4	8	no	—
118	C₂³×C₅	—	2	4	no	—
119	C₂³×C₅	—	2	2	no	—
120	C₂³×C₅	—	2	8	no	—
121	C₂³×C₅	—	2	2	no	—
122	C₂³×C₅	—	2	8	no	—
123	C₂³×C₅	—	4	2	no	—
124	C₂³×C₅	—	4	4	no	—
125	C₂³×C₅	—	4	2	no	—
126	C₂³×C₅	—	4	16	no	—
127	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
128	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
129	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
130	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
131	C₂³×C₅	C₃×#41	1	4	yes	—
132	C₂×C₄×C₅	—	2	4	no	—
133	C₂×C₄×C₅	—	4	4	no	—
134	C₂×C₄×C₅	—	4	4	no	—
135	C₂×C₄×C₅	—	4	4	no	—
136	C₂×C₄×C₅	—	4	8	no	—
137	C₂×C₄×C₅	—	4	4	no	—
138	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
139	C₂³×C₄	C₃×C₄×C₅	1	2	yes	complemented
140	C₂×C₂²⋊C₄	—	2	4	no	—
141	C₂×C₂²⋊C₄	—	2	4	no	—
142	C₂×C₂²⋊C₄	C₃×C₄×C₅	1	2	yes	complemented
143	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
144	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
145	C₂×C₃×C₅	—	2	4	no	—
146	C₂×C₃×C₅	—	2	4	no	—
147	C₂×C₃×C₅	—	2	2	no	—
148	C₂×C₃×C₅	—	4	2	no	—
149	C₂×C₃×C₅	#381	1	1	yes	characteristic
150	C₂×C₃×C₅	C₂×#99	1	2	yes	—
151	C₂³×C₃	—	2	2	no	—
152	C₂³×C₃	—	2	4	no	—
153	C₂³×C₃	—	2	2	no	—
154	C₂³×C₃	—	2	8	no	—
155	C₂³×C₃	—	2	8	no	—
156	C₂³×C₃	—	4	2	no	—
157	C₂³×C₃	—	4	4	no	—
158	C₂³×C₃	—	4	2	no	—
159	C₂³×C₃	—	4	16	no	—
160	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
161	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
162	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
163	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
164	C₂³×C₃	C₅×#41	1	4	yes	—
165	C₂×C₃×C₄	—	2	4	no	—
166	C₂×C₃×C₄	—	4	4	no	—
167	C₂×C₃×C₄	—	4	4	no	—
168	C₂×C₃×C₄	—	4	4	no	—
169	C₂×C₃×C₄	—	4	8	no	—
170	C₂×C₃×C₄	—	4	4	no	—
171	C₂²×C₅	—	2	8	no	—
172	C₂²×C₅	—	2	2	no	—
173	C₂²×C₅	—	2	2	no	—
174	C₂²×C₅	—	2	2	no	—
175	C₂²×C₅	—	2	4	no	—
176	C₂²×C₅	—	2	2	no	—
177	C₂²×C₅	—	2	4	no	—
178	C₂²×C₅	—	4	4	no	—
179	C₂²×C₅	—	4	16	no	—
180	C₂²×C₅	—	4	4	no	—
181	C₂²×C₅	C₃×#99	1	4	yes	—
182	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₅	C₃×#117	1	2	yes	—
184	C₂²×C₅	C₃×#123	1	4	yes	—
185	C₄×C₅	—	4	4	no	—
186	C₄×C₅	—	8	4	no	—
187	C₂⁴	—	2	4	no	—
188	C₂⁴	—	4	4	no	—
189	C₂⁴	C₂×C₃×C₄×C₅	1	1	yes	characteristic
190	C₂⁴	C₂×C₃×C₄×C₅	1	1	yes	characteristic
191	C₂⁴	C₃×C₅×D₄	1	4	yes	—
192	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	2	4	no	—
196	C₂²×C₄	—	4	4	no	—
197	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
198	C₂²⋊C₄	—	2	4	no	—
199	C₂²⋊C₄	—	2	4	no	—
200	C₂²⋊C₄	—	2	8	no	—
201	C₂²⋊C₄	—	4	8	no	—
202	C₃×C₅	#1819	1	1	yes	characteristic, direct product factor, Hall
203	C₂²×C₃	—	2	8	no	—
204	C₂²×C₃	—	2	2	no	—
205	C₂²×C₃	—	2	2	no	—
206	C₂²×C₃	—	2	2	no	—
207	C₂²×C₃	—	2	4	no	—
208	C₂²×C₃	—	2	2	no	—
209	C₂²×C₃	—	2	4	no	—
210	C₂²×C₃	—	4	4	no	—
211	C₂²×C₃	—	4	16	no	—
212	C₂²×C₃	—	4	4	no	—
213	C₂²×C₃	C₅×#99	1	4	yes	—
214	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₃	C₅×#117	1	2	yes	—
216	C₂²×C₃	C₅×#123	1	4	yes	—
217	C₃×C₄	—	4	4	no	—
218	C₃×C₄	—	8	4	no	—
219	C₂×C₅	—	2	4	no	—
220	C₂×C₅	—	2	4	no	—
221	C₂×C₅	—	2	2	no	—
222	C₂×C₅	—	4	2	no	—
223	C₂×C₅	C₃×#381	1	1	yes	characteristic
224	C₂×C₅	C₂×C₃×#99	1	2	yes	—
225	C₂³	—	2	2	no	—
226	C₂³	—	2	4	no	—
227	C₂³	—	2	2	no	—
228	C₂³	—	2	8	no	—
229	C₂³	—	2	8	no	—
230	C₂³	—	4	2	no	—
231	C₂³	—	4	4	no	—
232	C₂³	—	4	2	no	—
233	C₂³	—	4	16	no	—
234	C₂³	C₃×C₅×C₂²⋊C₄	1	2	yes	—
235	C₂³	C₃×C₅×C₂²⋊C₄	1	2	yes	—
236	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
237	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
238	C₂³	C₃×C₅×#41	1	4	yes	—
239	C₂×C₄	—	2	4	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	—	4	4	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	—	4	8	no	—
244	C₂×C₄	—	4	4	no	—
245	C₂×C₃	—	2	4	no	—
246	C₂×C₃	—	2	2	no	—
247	C₂×C₃	—	2	4	no	—
248	C₂×C₃	—	4	2	no	—
249	C₂×C₃	C₅×#381	1	1	yes	characteristic
250	C₂×C₃	C₂×C₅×#99	1	2	yes	—
251	C₅	C₃×#1819	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²	—	2	8	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	2	4	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	2	4	no	—
259	C₂²	—	4	4	no	—
260	C₂²	—	4	16	no	—
261	C₂²	—	4	4	no	—
262	C₂²	C₃×C₅×#99	1	4	yes	—
263	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²	C₃×C₅×#117	1	2	yes	—
265	C₂²	C₃×C₅×#123	1	4	yes	—
266	C₄	—	4	4	no	—
267	C₄	—	8	4	no	—
268	C₃	C₅×#1819	1	1	yes	characteristic, direct product factor, Sylow
269	C₂	—	2	4	no	—
270	C₂	—	2	2	no	—
271	C₂	—	2	4	no	—
272	C₂	—	4	2	no	—
273	C₂	C₃×C₅×#381	1	1	yes	characteristic
274	C₂	C₂×C₃×C₅×#99	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂⁴	C₂³×C₃×C₅
prime radical	C₂⁵×C₃×C₅	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂⁵×C₃×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₃×C₅×#342	C₂	semidirect
4. C₅×#1819	C₃	direct (N × H)
6. C₂³×C₃×C₄×C₅	C₄	semidirect
9. C₂×C₃×C₅×C₂²⋊C₄	C₄	semidirect
12. C₃×#1819	C₅	direct (N × H)
15. C₅×#342	C₂×C₃	semidirect
33. C₃×#342	C₂×C₅	semidirect
35. C₂³×C₄×C₅	C₃×C₄	semidirect
38. C₂×C₅×C₂²⋊C₄	C₃×C₄	semidirect
41. #1819	C₃×C₅	direct (N × H)
63. C₂³×C₃×C₄	C₄×C₅	semidirect
66. C₂×C₃×C₂²⋊C₄	C₄×C₅	semidirect
86. #342	C₂×C₃×C₅	semidirect
139. C₂³×C₄	C₃×C₄×C₅	semidirect
142. C₂×C₂²⋊C₄	C₃×C₄×C₅	semidirect
202. C₃×C₅	#1819	direct (N × H)
251. C₅	C₃×#1819	direct (N × H)
268. C₃	C₅×#1819	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#379	2
C₃×C₅×#342	2
C₅×#1819	3
C₃×#1819	5

Subgroups — C3×C5×#1819 #14274853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1819 #14274853